Next Part of Step II

Determining Peak Speed

©Dr. B. C. Paul 2000 revised 2008Note – The methods outlined here are typical of widely known

published engineering practices. The slides contain information taken specifically from the Caterpillar Performance Handbook and screen shots taken from the FPC computer program developed by

Caterpillar Equipment Company.

Identify Peak Vehicle Speeds

Peak Vehicle Speeds are a function of power a gearing and the resistance to vehicle travel

Resistances are• Grade resistance - overcoming (or

benefiting from gravity)• Rolling Resistance - from flexure of

tires and road• Wind Resistance

Review of Resistance

Wind Resistance not normally an issue for haul trucks - common practice to ignore

Grade Resistance• Good old physics problem where

break forces into components

2000 * sin (pheta)

Simplifying Grade Resistance

Tan (θ) = Rise / Run At Slopes less than about 20% Tan

(θ) = Sin(θ) Adjusting for Percentage Grade

instead of rise over run• 20 lbs/ton * % Grade = Grade Res.

We just took the Trig out of Grade Resistance Calculations

Rolling Resistance

Tires Sink into Ground - softer ground sink more

Tires Flatten Driving uphill out of a rut on a flat

tire spot Need to Know Underfoot conditions

and Type of Tire (Radial or Bias Ply)

Data Comes From an All Knowing Table

Reading the Table

Note that Table Gives either lbs/ton or % Grade

One way to treat rolling resistance is as a equivalent grade• Puts in the same units as grade

resistance so they are additive

Two Ways of Totaling Resistance

Equivalent Grade Method• Take Grade in %• Add Equivalent Grade for Rolling

Resistance Lbs Resistance method

• Tons Weight * 20 * % Grade• Plus Tons Weight * lbs/ton rolling

Note That with Down Hill both can be negative

Converting Between

To Convert Total Resistance in% Grade to lbs• Weight in tons * 20 * % eqiuv Grade -

lbs Resistance To Convert Total lbs Resistance to

% Grade• lbs / 20 / Weight in tons = % Grade

I’ll leave you in suspense wondering why we care

Getting Rolling Resistance for our FPC Example

FPC Uses the % Grade System

Assume I have a firm smoothRoad with tires not sinking inAbout 2.5% for bias ply tires

Entering into FPC

I had my gradeResistance from myHaulage profileDescription.

I added my rollingResistance of 2.5%

Peak Speed the Manual Way

Cat 773B 58 ton Mechanical Hauling Dolomite• 77 foot Turning Radius so it can make the 85

foot switch back• 44.6 yards heaped capacity * 2600 lbs/yd3 =

57.8 tons Good match

For the level Run• Grade Resistance is 0%• For hard pack earth 4.25%• Total is 4.25% Grade

Expressed as Lbs Resistance

Calculated as Lbs Resistance 43.5 tons Empty (from Cat Book) * 20 lbs/ton * 0% Grade 0 lbs Grade Resistance 43.5 tons * 85lbs/ton = 3697.5 lbs Total 3697.5 lbs Resistance

Peak Speed Established by Gradability Chart

Read Down the Grade LineTo the Intersection With theWeight Line

Read Over to Gear Curve

Read Down to the Speed

Speed is 40 mph in 7thGear

By the Rimpull or Lbs Resistance Method

Take Calculated RimpullRequirements (3698 lbs)and go to Rimpull Scale onChart

Read over to Gear Line

Read down to Speed

Conclude Peak Speed is40 mph in 7th Gear

Checking Other Peak Speeds

Ramp -10% grade• -10% Grade• + 4.25% Rolling Resistance• Total = - 5.75%

Convert to lbs• -5.75% * 20 * 87000/2000 = -5002.4

lbs Time to Go to the Chart

Holly Marshmellowed Jelly Beans! Theres no Scale for a

negative Grade!

Enter the Retarder Chart (No I didn’t Say Retarded)

Read Down the Net FavorableGrade to the Truck Weight Line

Read Over to Gear Curve

Read Down to the Speed

Conclude 40 mph in 7th Gear

Things to Note About Chart Reading

Some Charts Allow Either Grade or Rimpull Method• Cat Gradability Chart Allows Either

Some Allow Only One of the Two Methods• Cat Retarder Chart Allows Only

Favorable Grade Since it Varies by Manufacture, you

must know both methods

More Notes

For the Grade Method we read down either the empty or full weight line• For a volume limited truck the loaded

truck may not weigh full gross weight so you can’t use pre-printed line - you must use actual loaded weight

• Some bed liners alter empty weight

Manufactures Also Have Brake Performance Charts

Note That the Charts Differ in Braking Distance

Looking at the Total Negative Grade Distance in a cycle todetermine length - Not just grade for the chosen haul segment

How Does FPC do This

All the curves are programmed into FPC for Caterpillar Equipment

You have to input the curves for non-Caterpillar equipment.